How to stick OBJ vertices to other OBJ
Holding Ctrl will enable snapping, and snapping types can be picked here with the drop-down by the magnet that will toggle snapping.



You'll want vertex. Remember you can move along specific axes to get it snapping exactly the way you want.

Exactly what you'll want to do is change the snapping type to vertex. Then grab your ring part and move in the y axis, holding Ctrl to snap it to the rim of the cylinder.